ANGLES OF POLYGONS.

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Presentation transcript:

ANGLES OF POLYGONS

POLYGONS NOT POLYGONS

CONCAVE ON A PEGBOARD, A RUBBER BAND WILL COPY THE CONVEX SHAPE CONVEX

NAMES OF POLYGONS SIDES TRIANGLE 3 QUADRILATERAL 4 PENTAGON 5 HEXAGON 6 HEPTAGON 7 OCTAGON 8 NONAGON 9 DECAGON 10 DODECAGON 12 N – GON N

INTERIOR ANGLE SUM OF CONVEX POLYGONS 6 SIDES = 4 TRIANGLES FIND THE NUMBER OF TRIANGLES FORMED BY DIAGONALS FROM ONE VERTEX 6 SIDES = 4 TRIANGLES

INTERIOR ANGLE SUM 4 SIDES = 2 TRIANGLES FIND THE NUMBER OF TRIANGLES FORMED BY DIAGONALS FROM ONE VERTEX 4 SIDES = 2 TRIANGLES

INTERIOR ANGLE SUM 8 SIDES = 6 TRIANGLES FIND THE NUMBER OF TRIANGLES FORMED BY DIAGONALS FROM ONE VERTEX 8 SIDES = 6 TRIANGLES

IF N IS THE NUMBER OF SIDES THEN: INTERIOR ANGLE SUM EACH TRIANGLE HAS 180° IF N IS THE NUMBER OF SIDES THEN: INT ANGLE SUM = (N – 2 ) 180°

2 3 1 4 5 INT ANGLE SUM = ( 5 – 2 ) 180° ( 3 ) 180° = 540°

REGULAR POLYGONS REGULAR POLYGONS HAVE EQUAL SIDES AND EQUAL ANGLES SO WE CAN FIND THE MEASURE OF EACH INTERIOR ANGLE

N EACH INTERIOR ANGLE OF A REGULAR POLYGON = (N – 2 ) 180 REMEMBER N = NUMBER OF SIDES

REGULAR HEXAGON INT ANGLE SUM = (6 – 2 ) 180 = 720° EACH INT ANGLE = 720 = 120° 6

360° N EXTERIOR ANGLE SUM EXTERIOR ANGLE ANGLE OF A REGULAR POLYGON IS ALL POLYGONS HAVE AN EXTERIOR ANGLE SUM OF 360° THE MEASURE OF EACH EXTERIOR ANGLE OF A REGULAR POLYGON IS 360° N

NAME ____________ # SIDES ____8________ INT ANGLE SUM _________ EACH INT ANGLE _________ EXT ANGLE SUM _________ EACH EXT ANGLE _________

NAME Octagon # SIDES ____8________ INT ANGLE SUM 6 x 180 = 1080° EACH INT ANGLE 1080 / 8 = 135° EXT ANGLE SUM 360° EACH EXT ANGLE 360 / 8 = 45°

NAME DECAGON # SIDES ____________ INT ANGLE SUM _________ EACH INT ANGLE _________ EXT ANGLE SUM _________ EACH EXT ANGLE _________

NAME DECAGON # SIDES 10 INT ANGLE SUM 8 x 180 = 1440° EACH INT ANGLE 1440 / 10 = 144° EXT ANGLE SUM 360° EACH EXT ANGLE 360 / 10 = 36°

NAME ____________ # SIDES ____________ INT ANGLE SUM _________ EACH INT ANGLE _________ EXT ANGLE SUM _________ EACH EXT ANGLE 60______

NAME HEXAGON # SIDES 360 / 60 = 6 INT ANGLE SUM (6-2) X 180 = 720° EACH INT ANGLE 720 / 6 = 120° EXT ANGLE SUM 360° EACH EXT ANGLE 60